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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.quintic_hermite"></a><a class="link" href="quintic_hermite.html" title="Quintic Hermite interpolation">Quintic Hermite interpolation</a>
</h2></div></div></div>
<h4>
<a name="math_toolkit.quintic_hermite.h0"></a>
      <span class="phrase"><a name="math_toolkit.quintic_hermite.synopsis"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.synopsis">Synopsis</a>
    </h4>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">quintic_hermite</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">interpolators</span> <span class="special">{</span>

<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">quintic_hermite</span> <span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
    <span class="identifier">quintic_hermite</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">d2ydx2</span><span class="special">)</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">&lt;&lt;(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quintic_hermite</span> <span class="special">&amp;</span> <span class="identifier">m</span><span class="special">);</span>

    <span class="keyword">void</span> <span class="identifier">push_back</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">d2ydx2</span><span class="special">);</span>
<span class="special">};</span>

<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">cardinal_quintic_hermite</span> <span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
    <span class="identifier">cardinal_quintic_hermite</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">d2ydx2</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">x0</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dx</span><span class="special">);</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>

<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">cardinal_quintic_hermite_aos</span> <span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">using</span> <span class="identifier">Point</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
    <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">Point</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
    <span class="identifier">cardinal_quintic_hermite_aos</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&amp;&amp;</span> <span class="identifier">data</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">x0</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dx</span><span class="special">)</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>

    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>

<span class="special">}</span>
</pre>
<h4>
<a name="math_toolkit.quintic_hermite.h1"></a>
      <span class="phrase"><a name="math_toolkit.quintic_hermite.quintic_hermite_interpolation"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.quintic_hermite_interpolation">Quintic
      Hermite Interpolation</a>
    </h4>
<p>
      The quintic Hermite interpolator takes a list of possibly non-uniformly spaced
      abscissas, ordinates, and their velocities and accelerations which are used
      to construct a quintic interpolating polynomial between segments. This is useful
      for taking solution skeletons from ODE steppers and turning them into a continuous
      function, provided that the right-hand side <span class="emphasis"><em>f</em></span>(<span class="emphasis"><em>x</em></span>,
      <span class="emphasis"><em>y</em></span>) is differentiable along the solution path. The interpolant
      is <span class="emphasis"><em>C</em></span><sup>2</sup> and its evaluation has 𝑶(log(<span class="emphasis"><em>N</em></span>))
      complexity. An example usage is as follows:
    </p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">x</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">6</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">y</span><span class="special">{</span><span class="number">7</span><span class="special">,</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">,</span><span class="number">10</span><span class="special">,</span><span class="number">11</span><span class="special">,</span><span class="number">12</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">dydx</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">d2ydx2</span><span class="special">{</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">};</span>

<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">interpolators</span><span class="special">::</span><span class="identifier">quintic_hermite</span><span class="special">;</span>
<span class="keyword">auto</span> <span class="identifier">spline</span> <span class="special">=</span> <span class="identifier">quintic_hermite</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">x</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">y</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">dydx</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">d2ydx2</span><span class="special">));</span>
<span class="comment">// evaluate at a point:</span>
<span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">spline</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span>
<span class="comment">// evaluate derivative at a point:</span>
<span class="keyword">double</span> <span class="identifier">zprime</span> <span class="special">=</span> <span class="identifier">spline</span><span class="special">.</span><span class="identifier">prime</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span>
</pre>
<p>
      Periodically, it is helpful to see what data the interpolator has. This can
      be achieved via
    </p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">spline</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
</pre>
<p>
      Note that the interpolator is pimpl'd, so that copying the class is cheap,
      and hence it can be shared between threads. (The call operator and <code class="computeroutput"><span class="special">.</span><span class="identifier">prime</span><span class="special">()</span></code>
      are threadsafe.)
    </p>
<p>
      The interpolator can be updated in constant time. Hence we can use <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span></code>
      to do real-time interpolation.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">circular_buffer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="special">...</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">initial_x</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">};</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">initial_y</span><span class="special">{</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">,</span><span class="number">6</span><span class="special">,</span><span class="number">7</span><span class="special">};</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">initial_dydx</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">};</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">initial_d2ydx2</span><span class="special">{</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">};</span>
<span class="keyword">auto</span> <span class="identifier">circular_akima</span> <span class="special">=</span> <span class="identifier">quintic_hermite</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">initial_x</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">initial_y</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">initial_dydx</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">initial_d2ydx2</span><span class="special">));</span>
<span class="comment">// interpolate via call operation:</span>
<span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">circular_akima</span><span class="special">(</span><span class="number">3.5</span><span class="special">);</span>
<span class="comment">// add new data:</span>
<span class="identifier">circular_akima</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">0</span><span class="special">);</span>
<span class="comment">// interpolate at 4.5:</span>
<span class="identifier">y</span> <span class="special">=</span> <span class="identifier">circular_akima</span><span class="special">(</span><span class="number">4.5</span><span class="special">);</span>
</pre>
<p>
      <span class="inlinemediaobject"><object type="image/svg+xml" data="../../graphs/quintic_sine_approximation.svg"></object></span>
    </p>
<p>
      For equispaced data, we can use <code class="computeroutput"><span class="identifier">cardinal_quintic_hermite</span></code>
      or <code class="computeroutput"><span class="identifier">cardinal_quintic_hermite_aos</span></code>
      to get constant-time evaluation. This is useful in memory-constrained or performance
      critical applications where data is equispaced.
    </p>
<h4>
<a name="math_toolkit.quintic_hermite.h2"></a>
      <span class="phrase"><a name="math_toolkit.quintic_hermite.complexity_and_performance"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.complexity_and_performance">Complexity
      and Performance</a>
    </h4>
<p>
      The following google benchmark demonstrates the cost of the call operator for
      this interpolator:
    </p>
<pre class="programlisting"><span class="identifier">Run</span> <span class="identifier">on</span> <span class="special">(</span><span class="number">16</span> <span class="identifier">X</span> <span class="number">4300</span> <span class="identifier">MHz</span> <span class="identifier">CPU</span> <span class="identifier">s</span><span class="special">)</span>
<span class="identifier">CPU</span> <span class="identifier">Caches</span><span class="special">:</span>
  <span class="identifier">L1</span> <span class="identifier">Data</span> <span class="number">32</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
  <span class="identifier">L1</span> <span class="identifier">Instruction</span> <span class="number">32</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
  <span class="identifier">L2</span> <span class="identifier">Unified</span> <span class="number">1024</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
  <span class="identifier">L3</span> <span class="identifier">Unified</span> <span class="number">11264</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x1</span><span class="special">)</span>
<span class="identifier">Load</span> <span class="identifier">Average</span><span class="special">:</span> <span class="number">0.92</span><span class="special">,</span> <span class="number">0.64</span><span class="special">,</span> <span class="number">0.35</span>
<span class="special">--------------------------------------------------</span>
<span class="identifier">Benchmark</span>                                  <span class="identifier">Time</span>
<span class="special">--------------------------------------------------</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">8</span>                   <span class="number">8.14</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">16</span>                  <span class="number">8.69</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">32</span>                  <span class="number">9.42</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">64</span>                  <span class="number">9.90</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">128</span>                 <span class="number">10.4</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">256</span>                 <span class="number">10.9</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">512</span>                 <span class="number">11.6</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1024</span>                <span class="number">12.3</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">2048</span>                <span class="number">12.8</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">4096</span>                <span class="number">13.6</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">8192</span>                <span class="number">14.6</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">16384</span>               <span class="number">15.5</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">32768</span>               <span class="number">17.4</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">65536</span>               <span class="number">18.5</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">131072</span>              <span class="number">18.8</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">262144</span>              <span class="number">19.8</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">524288</span>              <span class="number">20.5</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1048576</span>             <span class="number">21.6</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">2097152</span>             <span class="number">22.5</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">4194304</span>             <span class="number">24.2</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">8388608</span>             <span class="number">26.6</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">16777216</span>            <span class="number">26.7</span> <span class="identifier">ns</span>
<span class="identifier">QuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span><span class="identifier">_BigO</span>                <span class="number">1.14</span> <span class="identifier">lgN</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">256</span>         <span class="number">5.22</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">512</span>         <span class="number">5.21</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1024</span>        <span class="number">5.21</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">2048</span>        <span class="number">5.32</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">4096</span>        <span class="number">5.33</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">8192</span>        <span class="number">5.50</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">16384</span>       <span class="number">5.74</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">32768</span>       <span class="number">7.74</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">65536</span>       <span class="number">10.6</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">131072</span>      <span class="number">10.7</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">262144</span>      <span class="number">10.6</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">524288</span>      <span class="number">10.5</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1048576</span>     <span class="number">10.6</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermite</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span><span class="identifier">_BigO</span>        <span class="number">7.57</span> <span class="special">(</span><span class="number">1</span><span class="special">)</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">256</span>      <span class="number">5.27</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">512</span>      <span class="number">5.26</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1024</span>     <span class="number">5.26</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">2048</span>     <span class="number">5.28</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">4096</span>     <span class="number">5.30</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">8192</span>     <span class="number">5.41</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">16384</span>    <span class="number">5.89</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">32768</span>    <span class="number">5.97</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">65536</span>    <span class="number">5.96</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">131072</span>   <span class="number">5.92</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">262144</span>   <span class="number">5.94</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">524288</span>   <span class="number">5.96</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;/</span><span class="number">1048576</span>  <span class="number">5.93</span> <span class="identifier">ns</span>
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span><span class="identifier">_BigO</span>     <span class="number">5.64</span> <span class="special">(</span><span class="number">1</span><span class="special">)</span>
</pre>
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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